Question

The surface area of a square pyramid can be calculated using the equation S=1/2lp+B%0D%0A𝑆%0D%0A=%0D%0A1%0D%0A2%0D%0A𝑙%0D%0A𝑝%0D%0A+%0D%0A𝐵%0D%0A. Rearrange the surface area equation for the quantity of interest B%0D%0A𝐵%0D%0A.

Answer 1

To rearrange the surface area equation for the quantity \( B \), we start with the original surface area equation of a square pyramid:

\[
S = \frac{1}{2} l p + B
\]

where:
- \( S \) is the surface area,
- \( l \) is the slant height,
- \( p \) is the perimeter of the base,
- \( B \) is the area of the base.

To isolate \( B \), we can subtract the \(\frac{1}{2} l p\) term from both sides of the equation. This gives us:

\[
B = S - \frac{1}{2} l p
\]

So, the rearranged equation for \( B \) is:

\[
B = S - \frac{1}{2} l p
\]